Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\bullet$$\bullet$ Tension in a muscle. Muscles are attached to bones bymeans of tendons. The maximum force that a muscle can exertis directly proportional to its cross-sectional area $A$ at thewidest point. We can express this relationship mathematicallyas $F_{\text { max }}=\sigma A,$ where $\sigma($ sigma) is a proportionality constant.Surprisingly, $\sigma$ is about the same for the muscles of all animals.and has the numerical value of $3.0 \times 10^{5}$ in SI units. (a) Whatare the SI units of $\sigma$ in terms of newtons and meters and also interms of the fundamental quantities $(\mathrm{kg}, \mathrm{m}, \mathrm{s})$ (b) In one setof experiments, the average maximum force that the gastrocne-mius muscle in the back of the lower leg could exert was meas-ured to be 755 $\mathrm{N}$ for healthy males in their midtwenties. Whatdoes this result tell us was the average cross-sectional area, in$\mathrm{cm}^{2},$ of that muscle for the people in the study?

a.The units of $\sigma$ must be either $\left[\mathrm{Nm}^{2}\right]$ or $\left[\mathrm{kg} / \mathrm{ms}^{2}\right]$b.$251.67 \times 10^{-5} \mathrm{m}^{2}$

Physics 101 Mechanics

Chapter 5

Applications of Newton's Law

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

Rutgers, The State University of New Jersey

Simon Fraser University

University of Sheffield

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

0:00

$\bullet$$\bullet$ Tension…

02:03

Muscles are attached to bo…

01:30

02:12

The femur of a human leg …

01:11

The large quadriceps muscl…

04:16

$\bullet$ Tendons. Tendons…

07:05

05:31

Tendons are strong elastic…

01:22

If you stand on one foot w…

02:37

Tendons. Tendons are stron…

03:22

08:56

. Muscle attachment. When …

All right. So for this problem, where basically given the equation f equals Sigma times, eh? We're sigma is some constant that were given in the problem and it has to do with muscle mass and someone. But you don't really need to know any of that as long as you know this equation for the question. So we are asked to find the units for Sigma. Now, we know that, um, the units of F foreign mutants and we noted the units of area our meter squared. If we're talking about S i units So for so the units of sigma must be Newton's over meter squared. And if we want to convert this into kilograms and seconds and meters, we can say that the units of Sigma are kilograms over second square times Peters and then for part B. We're told that the force is equal to 755 mutants and we're already given Sigma in the problem to be equal to 3.0 times 10 to the fifth kilograms per second squared times meters. And what we're trying to find is that area a cross section. So we have a is equal to a over sigma given by this equation right here. And if you calculate it out with 7 55 Newtons over 3.0 times 10 to the kilograms per second Squared tents meters. You get your answer. Your area is equal to 2 51 0.67 times 10 to the negative. Bye meter squared and that's it for this problem.

View More Answers From This Book

Find Another Textbook

03:48

\bullet A brass washer has an outside diameter of 4.50 $\mathrm{cm}$ with a …

02:07

$\cdot$ Compute the number of seconds in (a) an hour, (b) a 24 hour day, and…

04:06

$\bullet$ On a frictionless air track, a 0.150 $\mathrm{kg}$ glider moving a…

01:48

A gold wire 6.40 $\mathrm{m}$ long and of diameter 0.840 $\mathrm{mm}$ carri…

01:59

$\cdot$ $\cdot$ Animal energy. Adult cheetahs, the fastest of the greatc…

06:46

Atoms and nuclei. The atom helium (He) consists of two protons, two neutrons…

03:52

$\cdot$ On a highly polished, essentially frictionless lunch counter, a 0.50…

02:55

Stay dry! You tie a cord to a pail of water, and you swing the pail in a ver…

04:44

A rocket fires two engines simultaneously. One produces a thrust of 725 $\ma…

16:43

$\bullet$ The Cosmoclock 21 Ferris wheel in Yokohama City, Japan, has a diam…